"It doesn't let you watch videos because duckduckgo is letting you surf anon. Just allow the video to play on the duckduckgo site, or just head to their website, that simple."

The tradeoff of hitting play is that your view is tracked by google.
So the idea is to allow users to watch youtube videos without being tracked.

If DDG created temporary google account with which you can watch the video, because the account could be temporary and randomly assigned to different duck duck go users, the tracking data google gets from it could have no connection to you as an individual.

One way of implementing video view anonymity might be to launch a private browsing window, where duck duck go creates a new google account behind the scenes, and loads up the video. When the private browser window closes, so does the temporary account.

Another way to implement it would be to use a temp google account, play the video on a duck duck go server, and then "stream" the video to the current browser window, untrackable by Google. This might conflict with Youtube EULA though.

These are just two possible implementations. There may be simpler ways to do it, but the general idea is to use temporary accounts preventing google from tracking you when want to watch a video on the Duck Duck Go site.

There are existing services that offer temporary email accounts. So this is just applying that principle to to this use case.